I have a 2000 Ford Crown Vic police cruiser and replaced 2 starters within a month . One lasted only one day before I smelled it burn out. It shorted out; someone told me about maybe the alternator
You may want to check to see if the starter is receiving voltage after the engine has started. If the starter relay (often called the starter solenoid) is sticking, the starter is trying to run all the time. This will burn out a starter in a hurry.
Could also be the flywheel. A flywheel that has a broken tooth or is warped will keep the starter from disengaging…which will burn out a starter very quickly.
Rebuilt starters or new?
What may be happening is that power is being provided to the starter solenoid even when the key is in the RUN position.
This will keep the starter engaged and burn it up quickly.
About the only way to verify this would be to use a test light at the small wire at the starter solenoid and make sure that power is only provided in the RUN position.
This may be easier said than done since it appears to be intermittent.
One way to verify this would be to place a small 12 volt light in the car. Run one wire to ground and the other to the small wire at the starter solenoid. This light should only illuminate when the starter is activated. If it comes on, or stays on, at any time other than cranking then you know you have a relay, switch, or wiring glitch and this is the cause of the starter failures.
You could leave this light in place indefinitely until it’s determined that my theory is the cause of the problem.
I think this car uses a starter relay besides the solenoid and it’s possible the relay could be sticking, the ignition switch could be bad, or someone during it’s police past has been doing some dinking with the wiring.